Our research aimed to investigate the potential learning benefits to young children of implementing digital interactive multimodal technologies that provide both visual and haptic experiences in elementary mathematics classrooms. We studied the ways in which fourth-grade students collaboratively create collective strategies for solving…

Collaborative learning requires a lot of talk. Although not all student talk may be related to the task at hand, some off-task talk is actually productive, as it enables students to negotiate how they will work together, gain attention of fellow group members, and draw others into joining the work. Emma C. Gargroetzi, Rosa D. Chavez, Jen Munson,…

Developing textbooks of optimal quality is crucial for enriching the students' learning and understanding. This study examined fraction addition and subtraction problems in the U.S. and South Korean mathematics textbooks according to the types of denominators. In particular, we investigated Everyday Mathematics (EM) and South Korean mathematics…

When students are working together, some off-task conversations actually smooth the way to working together more effectively. While many assume that off-task talk is unproductive, our study revealed that students used off-task talk predominantly for productive purposes. We found that off-task talk supported student access to collaboration, and…

Is anything more refreshing than going for a nice, long swim? The math scenarios presented in this article will take the reader back to hot summer days and remind the reader what a cool dip in the water feels like. Solving these problems is enjoyable and encourages the solver to think of the many ways that math is all around--even in the middle of…

Research has demonstrated that providing labels helps children notice key features of examples. Much less is known about how different labels impact children's ability to make inferences about the structure underlying mathematical notation. We tested the impact of labeling decimals such as 0.34 using formal place-value labels ("3 tenths and 4…

Elementary students' difficulties with angles in geometry are well documented, but we know little about how they conceptualize angles while solving problems and how their thinking changes over time. In this study, we examined 26 third and fourth grade students completing a body-based angle task supported by the Kinect for Windows. We used…

Forty 4th and 9th grade students participated individually in tutorial interviews centered on a problem-solving activity designed for learning basic algebra mechanics through diagrammatic modeling of an engaging narrative about a buccaneering giant burying and unearthing her treasure on a desert island. Participants were randomly assigned to…

The teaching of problem-solving through the development of a problem-solving model was investigated in a Grade 4 mathematics classroom. Learners completed a questionnaire regarding their knowledge of mathematical problem-solving, their attitudes towards problem-solving, as well as their experiences in solving problems. Learners' responses revealed…

The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

A large body of research has shown that for novice learners, instruction that relies more heavily on worked examples than on problem solving, is more effective for learning as shown by higher test performance. Moreover, this beneficial effect is often obtained with less acquisition time and lower cognitive load during acquisition and test phase.…

NCTM's Process Standards support teaching that helps upper elementary level children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every intermediate-grades teacher the opportunity to explore each standard in depth. With language and examples that don't require prior math…

In this article, framed as a conversation, the authors discuss the learning resulting from a variety of geometry tasks they have conducted with their students. None of them are convinced that all the geometry tasks within the numeracy strategy prescribed in English schools are necessarily good for children or aimed at the right age range. Using…

"Progress in Mathematics[C] 2006" is a new core curriculum for students in kindergarten through grade 6. "Progress in Mathematics[C] 2006" differs substantively from "Progress in Mathematics[C] 2000" in both content and assessment material. "Progress in Mathematics[C] 2006" uses a sequence of systematic…